Abstract
We present a systematic construction of finite element exact sequences with a commuting diagram property for the de Rham complex in one-, two-, and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families of exact sequences for triangles and three for squares, and to uncover one new family of exact sequence for squares and two new families of exact sequences for general polygonal elements. We apply the construction in three-space dimensions to rediscover two families of exact sequences for tetrahedra, three for cubes, and one for prisms, and to uncover four new families of exact sequences for pyramids, three for prisms, and one for cubes.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1650-1688 |
| Number of pages | 39 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 55 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2017 Society for Industrial and Applied Mathematics.
Keywords
- Commuting diagrams
- Exact sequences
- Finite elements
- Polyhedral elements